Question: Rewrite as a simplified fraction. ${0.7\overline{73} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 773.7373...\\ 10x &= 7.7373...\end{align*}}$ Subtracting the two equations, we have: ${990x = 766}$ ${x = \dfrac{766}{990}} $ ${x = \dfrac{383}{495}} $